The Legislature is debating a North Carolina-style bill that would require transgender people to use bathrooms in public buildings that correspond with the sex on their birth certificate, as opposed to their gender identity. There are anti-abortion measures, like the one requiring the burial or cremation of fetal remains, and religious exception bills, like one that would allow pharmacists to refuse filling patient prescriptions based on their religious beliefs. There is the states’ rights push to hold a convention of states to tinker with and amend the United States Constitution, and there are several pro-gun efforts, including one to allow many Texans to carry a handgun without a license.

Every legislative session in Texas has a conservative tenor. Republicans control both chambers and every statewide elected office. But Republicans and Democrats say this session, the first in the Trump era, illustrated a shift to the right in a state that was already decidedly on that end of the political spectrum.

“There’s a sense the ball’s moving in our direction,” said Dick Armey, a former Texas congressman who was one of the architects of the 1994 Republican takeover of Congress. Mr. Armey, now 76, lives north of Fort Worth in Denton County, home to the University of North Texas and Texas Woman’s University. “In the city of Denton,” Mr. Armey added, “my guess is to get rid of sanctuary cities is probably appreciated everywhere but the faculty lounge.”

For Latino leaders, the signing of the ban on sanctuary cities represented a seismic shift. Latinos make up 39 percent of Texas’ population. The biggest school district in the state, the Houston Independent School District, is 62 percent Hispanic and only 8 percent white. Hispanics have shaped the very notion of what it means to be Texan, and many had pointed with pride at the recent past.

When California voters approved Proposition 187 in 1994, which was intended to deny public services like schools and hospital care to unauthorized immigrants, Texas resisted taking similar action. When Arizona passed a law known as S.B. 1070 in 2010, giving local law enforcement broad authority to detain people suspected of being in the country illegally, Texas again resisted.

That legacy, Hispanic leaders said, ended on Sunday, with the stroke of Mr. Abbott’s pen.

“This was the first time in recent memory that the Republican Party of Texas has crossed a red line with the Hispanic community,” said Julián Castro, the Obama-era secretary of the Department of Housing and Urban Development and the former mayor of San Antonio, contrasting Texas’ response with the earlier actions in California and Arizona. Referring to George W. Bush and Rick Perry, he added: “To their credit, at the time, Governors Bush and Perry exercised admirable restraint, instead of pitching to the worst instincts and feeding the base red meat on immigration. They refused to do it. Greg Abbott is a different story.”

As in other red states, Mr. Trump looms large in the ideological background of Texas politics. The bill banning sanctuary cities — which is known as Senate Bill 4 and is set to take effect in September — was backed by Lt. Gov. Dan Patrick, who was the Texas chairman of Mr. Trump’s campaign, as well as Mr. Abbott, who told Mr. Trump “I’m proud of you” when he visited the Oval Office in March.

Much of the ultraconservative tone this legislative session has been building in Texas for years, long before Mr. Trump’s campaign, and many lawmakers said the ban on sanctuary cities would have passed regardless of who was in the White House. In 2010, when Mr. Abbott was the state’s attorney general, he signed onto a legal brief filed in federal court defending Arizona’s S.B. 1070.

State Representative Rafael Anchia, a Democrat who is the chairman of the Mexican American Legislative Caucus in the State House, said the best evidence that Senate Bill 4 preceded the rise of Mr. Trump was the series of federal court rulings since 2011 in which the Texas Legislature was found to have intentionally discriminated against Hispanics and African-Americans. “This really doesn’t arise out of Trump, but my view is that it arises out of the movement that brought Trump,” Mr. Anchia said.

Democrats predict that Senate Bill 4 will energize Hispanic voters and mark the end of the Republican rule of Texas. On Tuesday, the American Civil Liberties Union in Washington issued what it called a “travel alert” for Texas, warning visitors to the state to expect “the possible violation of their constitutional rights when stopped by law enforcement.” In Austin and Houston, civil disobedience and more confrontational protest actions have met the bill. Such activity appeared to be one of the reasons Mr. Abbott signed the law late on Sunday without any notice to reporters.

Republicans dispute that the banning of sanctuary cities is discriminatory and defend it as anti-crime, not anti-immigrant.

“This bill is about the safety and security of Texans, and criticisms to the contrary are not based in the reality of what is written in the bill,” John Wittman, a spokesman for Mr. Abbott, said in a statement. “This bill will help keep dangerous criminals off our streets and protect innocent lives. For every ounce of criticism, there is a pound of praise from Texans who simply want laws to keep them safe.”

Republican leaders are so primed for lawsuits against the ban on sanctuary cities that the Texas attorney general, Ken Paxton, launched a pre-emptive strike, suing officials in Austin and the Mexican American Legal Defense and Educational Fund over the constitutionality of Senate Bill 4, before the officials and the group filed any suits of their own.